Banach-Tarski Theorem (also known as Paradox) is a mathematical statement which says that a sphere can be splitted into two (or an integer N...) spheres each equal to the original one.
Do you know some applications to Physics or other scientific disciplines?
See references.
Gianluca
R.M. French, The Banach-Tarski Theorem, The Mathematical Intelligencer, Vol. 10 (1988), No. 4, pp. 21-28
Stan Wagon, The Banach-Tarski Paradox, 1986
Banach-Tarski Paradox
Please let me know if the following references/sites are helpful to you:
1. Are there any applications of the Banach-Tarski paradox
https://www.quora.com/Are-there-any-applications-of-the-Banach...
The Banach-Tarski paradox has been called "the most suprising result of theoretical mathematics" (S.Wagon Mathematica in Action p.491). This is because of it...
2. Applications of Banach-Tarski Paradox to Probability Theory?
https://mathoverflow.net/questions/35989/applications-of-banach...
Applications of Banach-Tarski Paradox ... applications of B-T in physics. Physics uses mathematics as a framework to build models that correspond to the physical ...
Site reference:
https://mathoverflow.net/questions/35989/applications-of-banach-tarski-paradox-to-probability-theory
Dennis
Dennis Mazur
This is an interesting question.
First, the Banach-Tarski paradox is as follows: given two subsets in R^3, which are bounded and which have nonempty interiors, it is possible to cut A into a finite number of pieces which can be moved by rigid motions (translations and rotations) to form exactly B. That is a paradox!
https://people.math.umass.edu/~weston/oldpapers/banach.pdf
Assuming that this can be done with a pair of spheres A and B, here is a suggested physical application:
Let A, B be finite, bounded spheres with nonempty interiors. Assume A,B are balloons. Fill B with water and then measure the amount of water B holds. Draining the water from either A or B is analogous to cutting A or B into pieces (water leaving a balloon makes a balloon smaller). Then fill A with water with the same amount of water that B holds. The action of expanding A with water resembles the translations and rotations one would need to make abstractly in "porting" A over to B.
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